A Unified Geometric Scale of Fundamental Interactions through the Fine-Structure Constant in the Ontopole Field Model

AbstractThe fine-structure constant α ≈ 1/137.036 is one of the most fundamental dimensionlessquantities in physics. In the Ontopole field model, α is interpreted not as a local propertyof the hydrogen atom, but as a universal geometric parameter that determines the strengthof all fundamental interactions.We show that α arises naturally from the dynamics of an unclosed vortex in a 12-dimensional field and can be expressed through a single parameter — the effective numberof vortex windings n. The proposed relationα−1(n) = 2πn −π16− 1reproduces the vacuum value α−1(22) ≈ 137.034 with high accuracy. The running of α isunderstood as a change in the effective winding number under different energy conditions,leading to a stepwise behavior.Within this framework, the strong (n ≈ 0.35), weak (n ≈ 5), electromagnetic (n = 22),and gravitational (n → ∞) interactions are unified on a single geometric scale of vortexwindings. The phase deficit π/16, originating from four successive acts of binary phasequantization, is identified as the geometric origin of electric charge.The model offers a coherent geometric picture that connects the numerical value of α, itsenergy dependence, and the hierarchy of fundamental forces within one theoretical framework.Keywords: fine-structure constant, fundamental interactions, Ontopole field model, vortexdynamics, phase deficit, running coupling constant, geometric unification